The amount of information to be transmitted via optical communication is steadily increasing. In order to match up to such an increase in the amount of information, attempts are being made such as an increase in signal speed and an increase in the number of channels by wavelength-division multiplexing. A next-generation 100-Gbps digital coherent transmission technology which is intended for high-speed information communication, in particular, attempts to double the amount of information to be communicated per unit of time by polarization-division multiplexing. Note that “polarization-division multiplexing” herein refers to superimposing pieces of information of two polarized waves (such as TM polarized wave and TE polarized wave) which have respective electric fields orthogonal to each other.
However, in a case where polarization-division multiplexing is carried out, a configuration of an optical modulator becomes complex. This results in problems such as increases in device size and production costs. In view of the circumstances, attempts have been made to realize an optical modulator that carries out polarization-division multiplexing by use of a substrate-type waveguide element including a silicon waveguide which can be easily processed and which is capable of a reduction in device size by integration and capable of a reduction in production costs by mass production.
The optical modulator to carry out polarization-division multiplexing is equipped with, for example, a polarized beam combiner which combines together a TM polarized wave including a piece of information and a TE polarized wave including another piece of information. As a technology for causing a substrate-type waveguide element to serve as such a polarized beam combiner, for example, a technology disclosed in Non-Patent Literature 1 is known.
FIG. 9 shows a substrate-type waveguide element 5 disclosed in Non-Patent Literature 1. (a) of FIG. 9 is a cross-sectional view of the substrate-type waveguide element 5. (b) and (c) of FIG. 9 are plan views of the substrate-type waveguide element 5 (a lower cladding 51 and an upper cladding 52 are not illustrated).
As illustrated in (a) of FIG. 9, the substrate-type waveguide element 5 includes (i) a lower cladding 51 made of silica (SiO2), (ii) two cores 53 and 54, each made of silicon (Si), which are provided on the lower cladding 51, (iii) an upper cladding 52, made of silica, which is provided on the lower cladding 51 so as to bury the two cores 53 and 54. The two cores 53 and 54 have congruent rectangular cross sections (see (a) of FIG. 9), and are provided so that their respective side surfaces are in the proximity of each other in a partial segment (segment enclosed in dotted lines; see (b) and (c) of FIG. 9). Hereinafter, the segment, in which the respective side surfaces of the two cores 53 and 54 are in the proximity of each other, will be also referred to as “parallel segment.”
The substrate-type waveguide element 5 is designed so that a length L of the parallel segment, in which the two cores 53 and 54 run parallel to each other, matches a coupling length with respect to a TM0 polarized wave. Therefore, as illustrated in (b) of FIG. 9, inputting a TM0 polarized wave and a TE0 polarized wave into the first core 53 causes the TM0 polarized wave to be outputted from the second core 54 and causes the TE0 polarized wave to be outputted from the first core 53. In other words, the substrate-type waveguide element 5 serves as a polarized beam splitter that separates the TM0 polarized wave and the TE0 polarized wave from each other. In addition, as illustrated in (c) of FIG. 9, inputting a TM0 polarized wave into the first core 53 and inputting a TE0 polarized wave into the second core 54 causes the TM0 polarized wave and the TE0 polarized wave to be outputted from the second core 54. In other words, the substrate-type waveguide element 5 serves also as a polarized beam combiner that combines the TM0 polarized wave and the TE0 polarized wave together.
Note that “TE polarized wave” herein refers to a polarization mode having an electric field whose main component oscillates in a direction (i) orthogonal to a traveling direction of light propagating in a core and (ii) parallel to a direction in which a boundary surface between an upper cladding and a lower cladding extends. In particular, a TE polarized wave having a maximum effective refractive index is referred to as “TE0 polarized wave.” Note also that “TM polarized wave” herein refers to a polarization mode having an electric field whose main component oscillates in a direction (i) orthogonal to a traveling direction of light propagating in a core and (ii) perpendicular to a direction in which a boundary surface between an upper cladding and a lower cladding extends. In particular, a TM polarized wave having a maximum effective refractive index is referred to as “TM0 polarized wave.”
As described above, the substrate-type waveguide element 5 is configured such that (i) a TM0 polarized wave inputted into the first core 53 is outputted from the second core 54 whereas a TE0 polarized wave inputted into the first core 53 is outputted mainly from the first core 53 and (ii) a TE0 polarized wave inputted into the second core 54 is outputted mainly from the second core 54. An explanation of the configuration is as follows:
First, a coupling efficiency T of the substrate-type waveguide element 5 with respect to each polarization mode (a polarization mode to be focused will be hereinafter referred to as “target mode”) is obtained, as a function of the length L of the parallel segment in which the two cores 53 and 54 run parallel to each other, by Equation (1) at large. Note that “coupling efficiency” herein means a ratio of power of a target mode outputted from the second core 54 to power of the target mode inputted into the first core 53 (or a ratio of power of a target mode outputted from the first core 53 to power of the target mode inputted into the second core 54). The definitions of “F” and “q” in Equation (1) are as shown in Equation (2) and Equation (3).
                    [                  Equation          ⁢                                          ⁢                      (            1            )                          ]                                                            T        =                  F          ⁢                                          ⁢                                    sin              2                        ⁡                          (              qL              )                                                          (        1        )                                [                  Equation          ⁢                                          ⁢                      (            2            )                          ]                                                            F        =                  1                      1            +                                          (                                  δ                  χ                                )                            2                                                          (        2        )                                [                  Equation          ⁢                                          ⁢                      (            3            )                          ]                                                            q        =                                            χ              2                        +                          δ              2                                                          (        3        )            
Note that δ is a coefficient defined by Equation (4), wherein (i) a difference between an effective refractive index of a target mode to be guided through the first core 53 (effective refractive index in a case where the second core 54 does not exist) and an effective refractive index of a target mode to be guided through the second core 54 (effective refractive index in a case where the first core 53 does not exist) is ΔN1 and (ii) a wavelength of the target mode is λ.
                    [                  Equation          ⁢                                          ⁢                      (            4            )                          ]                                                            δ        =                              π            λ                    ⁢          Δ          ⁢                                          ⁢                      N            I                                              (        4        )            
x (referred to as “coupling coefficient”) is obtained by Expression (5), wherein (i) a refractive index distribution of a core cross section in a case where only the first core 53 exists (in a case where the second core 54 does not exist) is N1, (ii) a refractive index distribution of core cross sections in a case where the first core 53 and the second core 54 both exist is N, (iii) an electric field vector of a target mode to be guided through the first core 53 is E1, and (iv) an electric field vector of a target mode to be guided through the second core 54 is E2.[Expression 5]χ∝∫−∞∞∫−∞∞(N2−N12)E1*·E2dxdy  (5)
Note that the coupling coefficient x is obtained by integrating, at the core cross sections, an inner product of the electric field vector E1 of the target mode to be guided through the first core 53 and the electric field vector E2 of the target mode to be guided through the second core 54. Therefore, a larger amount by which the target mode guided through each of the two cores 53 and 54 escapes into a cladding results in a larger coupling coefficient x. A high degree of optical coupling between the target modes guided through the two cores 53 and 54 clearly indicates a large value of the coupling coefficient x defined by Expression (5).
In addition, sin(qL) shown in Equation (1) becomes 1 when the length L of the parallel segment, in which the two cores 53 and 54 run parallel to each other, matches Lc defined by Equation (6). The Lc defined by Equation (6) is referred to as “coupling length.” Note that the coupling length Lc is obtained for each polarization mode. Hereinafter, a coupling length with respect to a TM0 polarized wave will be described as Lc (TM0), and a coupling length with respect to a TE0 polarized wave will be described as Lc (TE0).
                    [                  Equation          ⁢                                          ⁢                      (            6            )                          ]                                                                      L          C                =                              π                          2              ⁢              q                                =                      π                          2              ⁢                                                                    χ                    2                                    +                                      δ                    2                                                                                                          (        6        )            
The following description is an explanation of the configuration of the substrate-type waveguide element 5 such that a TM0 polarized wave inputted into the first core 53 is outputted from the second core 54. According to the substrate-type waveguide element 5, the two cores 53 and 54 have identical cross-sectional shapes. This causes the difference ΔN1 in effective refractive index between the two cores 53 and 54 with respect to each polarization mode to be 0. Therefore, “F” shown in Equation (1) becomes 1. In addition, the substrate-type waveguide element 5 is designed so that the length L of the parallel segment, in which the two cores 53 and 54 run parallel to each other, matches the coupling length Lc (TM0) with respect to a TM0 polarized wave. This causes sin(qL) shown in Equation (1) to be 1. Therefore, the coupling efficiency T (TM0) with respect to the TM0 polarized wave becomes 1. This means that a TM0 polarized wave inputted into the first core 53 is outputted from the second core 54 without exception.
Meanwhile, the coupling length Lc with respect to each polarization mode has wavelength dependency. For example, a longer wavelength λ results in a larger amount by which a TM0 polarized wave guided through each of the two cores 53 and 54 escapes. Therefore, a longer wavelength λ causes optical coupling between the TM0 polarized waves guided through the two cores 53 and 54 to be stronger, and consequently causes the coupling length Lc (TM0) with respect to the TM0 polarized waves. Note that the length L of the parallel segment, in which the two cores 53 and 54 run parallel to each other, match the coupling length Lc (TM0) with respect to a TM0 polarized wave having a design wavelength which has been predetermined. Therefore, it is not possible to avoid losing a TM0 polarized wave having a wavelength outside the design wavelength. However, stronger optical coupling between the TM0 polarized waves guided through the two cores 53 and 54 causes the wavelength dependency of the coupling length Lc (TM0) to be small. Therefore, the optical coupling between the TM0 polarized waves guided through the two cores 53 and 54 is preferably strong in order to restrict, to a low amount, an amount of loss of a TM0 polarized wave having a wavelength outside the design wavelength.
The following is an explanation of the configuration of the substrate-type waveguide element 5 such that (i) a TE0 polarized wave inputted into the first core 53 is outputted mainly from the first core 53 and (ii) a TE0 polarized wave inputted into the second core 54 is outputted mainly from second core 54. A coupling length Lc (TE0) with respect to a TE0 polarized wave does not match but is longer than a coupling length Lc (TM0) with respect to a TM0 polarized wave. Therefore, as shown in Equation (7), a coupling efficiency T (TE0) with respect to a TE0 polarized wave is smaller than a coupling efficiency T (TM0) with respect to a TM0 polarized wave (TM0=1). This (i) causes only a part of a TE0 polarized wave inputted into the first core 53 to be outputted from the second core 54 and (ii) causes a remaining part of the TE0 polarized wave to be outputted from the first core 53. Likewise, only part of a TE0 polarized wave inputted into the second core 54 is outputted from the first core 53, and a remaining part of the TE0 polarized wave is outputted from the second core 54.
                    [                  Equation          ⁢                                          ⁢          7                ]                                                                      T          ⁡                      (                          TE              ⁢                                                          ⁢              0                        )                          =                                            sin              2                        ⁡                          (                                                π                  2                                ⁢                                                      Lc                    ⁡                                          (                                              TM                        ⁢                                                                                                  ⁢                        0                                            )                                                                            Lc                    ⁡                                          (                                              TE                        ⁢                                                                                                  ⁢                        0                                            )                                                                                  )                                <          1                                    (        7        )            